EXISTENCE OF POSITIVE PERIODIC SOLUTION TO A CLASS OF NEUTRAL DELAY COMPETITION MODEL

By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.     

拟线性双曲组一类非局部混合初-边值问题的半整体C1解

在研究拟线性弦振动方程带第三类边值问题的精确边界能控性时,出现了拟线性双曲组一类非局部混合初-边值问题.论文先证明该类非局部混合问题局部C1解的存在惟一性,并考察其存在高度的性质,进而利用一致先验估计证明半整体C1解的存在惟一性,并以此为基础研究相应问题的精确边界能控性,最后为便于应用,将论文的结论写成了可化约方程组的情形.     

类p-Laplace方程的无穷多解的存在性

本文研究了类p-Laplace方程,利用证明其对应的变分泛函满足Cerami条件,得到了无穷多个大能量解的存在性,推广并改进了已有结果.     

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.     

The Cauchy Problems and Global Solutions to the Deybe System and Burgers＇ Equations in Pseudomeasure Spaces

In this paper we consider the Cauchy problems of Burgers＇ equations and the Deybe system. Their existence and uniqueness of the time-global solutions for small initial data in some pseudomeasure spaces are obtained. The asymptotic stability of small solutions is proved. As an immediate result the existence and uniqueness of the self-similar solutions are also obtained provided the initial data satisfy the self-similar structures.     

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first–order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution. Research partially supported by Ministerio de Educación y Ciencia and FEDER, Project MTM2004-06652-C03-01, and by Xunta de Galicia and FEDER, Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN     

弱耗散Camassa-Holm方程解的Blowup及衰减性质

本文研究弱耗散Camassa-Holm方程的Cauchy问题,由Kato理论得到了局部适定性的结果,证明了解的blowup及整体存在性,并证明了当耗散系数满足适当条件时,整体解具有衰减性质.     

一类消失项带有时间导数的对流方程

本文在Duijn等的基础上研究了方程ht f(h)x=εhxx ε2τ1hxxt ε2τhxxx的行波解,其中f(h)∈C2(R)是满足所谓凹凸性的任意已知函数,得出了在不同的τ1,τ2条件下,该方程行波解的存在性条件和唯一性条件,并利用行波解得到上述方程的解,从而得到了对流方程的弱解,并分析了对流方程的多解性.     

矩阵方程X-A~*X~qA=Q(q>0)的Hermite正定解

本文讨论了矩阵方程X-A*XqA=Q(q>0)的Hermite正定解,给出了q>1时解存在的必要条件,存在区间,以及迭代求解的方法．证明了0相似文献   

矩阵方程AXB+CYD=E的对称极小范数最小二乘解

对于任意给定的矩阵A∈Rm×n,B∈Rn×s,C∈Rm×k,D∈Rk×s,E∈Rm×s,本文利用矩阵的Kmnecker积和Moore-Penrose广义逆,研究矩阵方程AXB CYD=E的对称极小范数最小二乘解,得到了解的表达式．并由此给出了矩阵方程AXB=C的双对称极小范数最小二乘解的表达式．此外,我们还给出了求矩阵方程AXB=C的双对称极小范数最小二乘解的数值算法和数值例子．